Binary relation in a cartesian product

In summary, a binary relation in a cartesian product is a way of relating elements from two different sets by creating ordered pairs. Its purpose is to show the relationship between the two sets and can be denoted using the notation R ⊆ A × B. Examples of binary relations include "is greater than," "is a member of," and "is equivalent to." It differs from a function in that it can relate one element to multiple elements in the codomain and does not have to satisfy the vertical line test.
  • #1
nafees ahmad
4
0
How many binary relation can be formed from the cartesian product below:
A = { 1 , 2 } & B = {a }
i know there are two ordered pairs in this cartesian products A * B.
i also know that there are 4 binary realtions. could someone please write
those four relations for me, i am really confused here.
 
Physics news on Phys.org
  • #2
{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.
 
  • #3
HallsofIvy said:
{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.

I'd imagine, they're actually something more like these: {}, {(1, a)}, {(2, a)}, and {(1, a), (2, a)}...
 
  • #4
thanx. i really apprecite u for this
 

What is a binary relation in a cartesian product?

A binary relation in a cartesian product is a way of relating elements from two different sets, known as the domain and codomain, by creating ordered pairs where the first element comes from the domain and the second element comes from the codomain.

What is the purpose of using a binary relation in a cartesian product?

The purpose of using a binary relation in a cartesian product is to show the relationship between elements from two different sets. It can help to identify patterns, connections, and dependencies between the two sets.

How is a binary relation denoted in a cartesian product?

A binary relation in a cartesian product is denoted using the notation R ⊆ A × B, where R is the relation, A is the domain, and B is the codomain.

What are some examples of binary relations in a cartesian product?

Examples of binary relations in a cartesian product include "is greater than," "is a member of," and "is equivalent to." For example, the relation "is greater than" can be represented as {(1,2), (3,4), (5,6)}, indicating that 1 is greater than 2, 3 is greater than 4, and 5 is greater than 6.

How is a binary relation different from a function in a cartesian product?

A binary relation can relate one element from the domain to multiple elements in the codomain, while a function in a cartesian product can only relate one element from the domain to one element in the codomain. Additionally, a function must satisfy the vertical line test, whereas a binary relation does not have this requirement.

Similar threads

I Supremum of a set, relations and order
    • Set Theory, Logic, Probability, Statistics
2
Replies
35
Views
542
I Cartesian Product Definitions
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
I Question Regarding Definition of Tensor Algebra
    • Linear and Abstract Algebra
Replies
10
Views
352
MHB Sets so that the cartesian product is commutative
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
MHB Binary Relations and Equivalence Classes | Proving R is an Equivalence Relation
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
I New Preprint on Wide Binaries Supports MOND
    • Beyond the Standard Models
Replies
14
Views
2K
A Probability of finding a k-subset in a d-dimensional random
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
932
MHB Nonreflexive Relation ....
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
3K
I Understanding Special Relativity and Coordinates
    • Special and General Relativity
Replies
4
Views
913
Cartesian product of index family of sets
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top